How do rigs relate to weights?
Some tips:


a good topology is very important for smooth joints transformations (try to model your finger as pictured below and you'll see how smooth it bends)



a proper mesh weights assigment is crucial for realistic bend movement (I suggest you using the With Automatic Weights parenting option. Select your mesh, then the bones and press Ctrl+P-->With Automatic Weights. This'll automatically aassign the proper, blended weights for all bones)